Provide a rigorous critique of each step of the following argument which appeared in a recent submission to the European Conference on AI
 
“Given two admissible heuristics h1 and h2 where h1(n) >= h2(n) for all nodes n. it is obvious that A* using h1 will be more efficient than A* using h2. Now suppose I am given an admissible heuristic h2. If one can find a constant c such that the heuristic h1(n) = h2(n) + c is still admissible, then searching with h1 is better than searching with h2.”